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Pascal’s Triangle and its Secrets – Introduction

This is the first in a series of guest posts by David Benjamin, exploring the secrets of Pascal’s Triangle.

The triangle of Natural numbers below contains the first seven rows of what is called Pascal’s triangle. Each row begins and ends with the number 1, and each of the remaining numbers, from the third row onwards, is the sum of the two numbers ‘above’:

Pascal's triangle, with three triangles of numbers (two in one line, that sum to the one between them on the line below) highlighted in colour
The first seven rows of Pascal’s triangle, showing some pairs and their sums below (highlighted)
Animation showing numbers in Pascal's triangle being generated by adding the pair above
Generating the triangle